Method for determining a longitudinal vehicle by compensating individual wheel speeds

ABSTRACT

A control system ( 24 ) for controlling a safety system ( 40 ) of an automotive vehicle includes a plurality of wheel speed sensors ( 30 ) generating a plurality of wheel velocity signals, a steering angle sensor ( 39 ) generating a steering actuator angle signal, a yaw rate sensor ( 28 ) generating a yaw rate signal, a lateral acceleration sensor ( 32 ) generating a lateral acceleration signal and a controller ( 26 ). The controller ( 26 ) generates a final reference vehicle velocity in response to the plurality of wheel speed signals, the steering angle signal, the yaw rate signal and the lateral acceleration signal. The controller ( 26 ) controls the safety system in response to the final reference vehicle velocity.

CROSS REFERENCE TO RELATED APPLICATIONS

The present invention claims priority to provisional application No.60/450,248, filed on Feb. 26, 2003, filed simultaneously herewith, thedisclosure of which is incorporated by reference.

BACKGROUND OF INVENTION

The present invention relates generally to dynamic control systems forautomotive vehicles and, more specifically to a system that compensateswheel speed sensor signals to determine a vehicle reference velocity.

It is a well-known practice to control various operating dynamics of amotor vehicle to achieve active safety. Examples of active safetysystems include traction control, yaw stability control and rollstability control systems. A more recent development has been to combineall the available subsystems to achieve better vehicle safety anddynamics performance. The effective operation of the various controlsystems requires high-accuracy and fast-response-times in thedetermination of the operating states of the vehicle, regardless of roadconditions and driving conditions. Such vehicle operating states includethe vehicle longitudinal, lateral and vertical velocities measured alongthe body-fixed longitudinal, lateral and vertical axes, the attitude ofthe vehicle body, and the travel course of the vehicle.

One piece of basic information that forms the aforementioned vehiclestate estimation is the linear velocity of the rotating centers of thefour wheels. For example, this information can be used to assess thewheel slip used in anti-brake-lock controls and traction controls and toestimate the longitudinal velocity of the vehicle. In order to obtainthe linear corner velocities, the wheel speed sensors are used. Thewheel speed sensors output the products of the wheel rotational speedsand the rolling radii. The wheel rotational speeds are directly measuredand the rolling radii are assumed their normal values. During dynamicmaneuvers, the variations of the wheel normal loading will affect therolling radii. Hence, the nominal rolling radii may not reflect theactual rolling radii and thus cause errors in the calculation of thewheel speeds.

It would, therefore be desirable to provide a more accurate way in whichto determine the vehicle speed taking into consideration changes inrolling radii.

SUMMARY OF INVENTION

The present invention provides an improved determination of theindividual wheel speeds. In the present invention the individual wheelspeed calculations may be compensated for by learning the rolling radiiof the wheels. Thus, a more accurate determination of the vehiclereference velocity or the longitudinal velocity may be determined.

In one aspect of the invention, a control system 24 for controlling asafety system 40 of an automotive vehicle includes a plurality of wheelspeed sensors 30 generating a plurality of wheel velocity signals, asteering angle sensor 39 generating a steering actuator angle signal, ayaw rate sensor 28 generating a yaw rate signal, a lateral accelerationsensor 32 generating a lateral acceleration signal and a controller 26.The controller 26 generates a final reference vehicle velocity inresponse to the plurality of wheel speed signals, the steering anglesignal, the yaw rate signal and the lateral acceleration signal. Thecontroller 26 controls the safety system in response to the finalreference vehicle velocity.

In a further aspect of the invention, a method of controlling a safetysystem for an automotive vehicle having a plurality of wheels includesdetermining a plurality of wheel velocities for the plurality of wheels,determining a preliminary longitudinal velocity of the vehicle from theplurality of wheel velocities, determining a plurality of correctionfactors for the plurality of wheel velocities for the plurality ofwheels, determining a vehicle reference velocity in response to theplurality of correction factors, the plurality of wheel velocities andthe preliminary longitudinal velocity, determining a lateralacceleration, determining a vehicle reference velocity correction factorin response to the lateral acceleration, determining a final referencevelocity in response to the vehicle reference velocity correction factorand the vehicle reference velocity, and controlling the safety system inresponse to the final reference velocity.

Other advantages and features of the present invention will becomeapparent when viewed in light of the detailed description of thepreferred embodiment when taken in conjunction with the attacheddrawings and appended claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a top view of a motor vehicle illustrating various operatingparameters of a vehicle experiencing a turning maneuver on a roadsurface.

FIG. 2 is a side view of a motor vehicle wheel illustrating variousoperating parameters of the wheel.

FIG. 3 is a block diagram showing a portion of a microprocessorinterconnected to sensors and controlled devices, which may be includedin a system according to the present invention.

FIG. 4 is a control system block diagram in accordance with the presentinvention.

DETAILED DESCRIPTION

In the following figures the same reference numerals will be used toillustrate the same components.

Referring now to FIG. 1, various operating parameters and variables usedby the present invention are illustrated as they relate to theapplication of the present invention to a ground based motor vehicle 10having wheels 12, 14, 16, 18. Those skilled in the art will immediatelyrecognize the basic physics represented by these illustrations, therebymaking the adaptation to different types of vehicles easily within theirreach. A lateral and longitudinal velocities of the center of gravityare denoted as V_(x) and V_(y) a yaw angular rate is denoted as ω_(x), afront wheel steering angle is denoted as δ, lateral acceleration isrepresented by a_(y), longitudinal acceleration is represented by a_(x).

Using those vehicle motion variables, the velocities of the vehicle atthe four corner locations, where the wheels are attached to the vehicle,can be calculated in the following form which are projected along thebody fixed longitudinal and lateral directionsV_(lfx)=V_(x)−ω_(z)t_(f), V_(lfy)=V_(y)+ω_(z)l_(f)V_(rfx)=V_(x)+ω_(z)t_(f), V_(rfy)=V_(y)+ω_(z)l_(f)V_(lrx)=V_(x)−ω_(z)t_(r), V_(lry)=V_(y)−ω_(z)l_(r) V_(rrx)=V_(y)+ω_(z)t_(r), V_(rry)=V_(y)−ω_(z)l_(r)   (1)

where t_(f) and t_(r) are the half tracks for the front and rear axles,l_(f) and l_(r) are the distances between the center of gravity of thevehicle and the front and rear axles. The variables V_(lf), V_(rf),V_(lr) and V_(rr) are the linear velocities of the four corners alongthe wheel heading directions (left front, right front, left rear andright rear, respectively), which can be calculated as in the followingV_(lf)=V_(lfx) cos (δ)+V_(lfy) sin (δ)V_(rf)=V_(rfx) cos (δ)+V_(rfy) sin (δ)V_(lr)=V_(lrx)V_(rr)=V_(rrx)   (2)

Referring now to FIG. 2, vehicle corner velocity along the wheellongitudinal direction is equal to the sum of the contact patch slipvelocity v_(cp) and the product of the wheel rotational rate ω_(whl) andits rolling radius r₀.

Referring now to FIG. 3, stability control system 24 has a controller 26used for receiving information from a number of sensors which mayinclude a yaw rate sensor 28, speed sensors 30 (at each wheel), alateral acceleration sensor 32, a roll rate sensor 34, a steering angle(hand wheel position) sensor 35, a longitudinal acceleration sensor 36,a pitch rate sensor 37, and steering angle position sensor 39. Steeringangle position sensor 39 senses the position of the steered road wheels.Lateral acceleration, longitudinal acceleration, yaw rate, rollorientation and speed may also be obtained using a global positioningsystem (GPS). Based upon inputs from the sensors, controller 26 controlsthe safety system 40. Depending on the desired sensitivity, the type ofsafety system and various other factors, not all the sensors 28-39 maybe used in a commercial embodiment. Other factors may be obtained fromthe sensors such as the surface mu and the vehicle side slip angle, β.

Roll rate sensors 34 and pitch rate sensors 37 may sense the rollcondition to be used with a rollover control system as an extension ofthe present application.

Safety system 40 may be a number of types of safety systems including aroll stability control system, a yaw control system, antilock brakes,traction control, airbags, or active suspension system.

Safety system 40 if implemented may control a position of a front rightwheel actuator, a front left wheel actuator, a rear left wheel actuator,or a right rear wheel actuator. Although, as described above, two ormore of the actuators may be simultaneously controlled as one actuator.Based on the inputs from sensors 28 through 39, controller 26 determinesthe vehicle dynamic conditions and controls the safety system.Controller 26 may also use brake control coupled to front right brakes,front left brakes, rear left brakes, and right rear brakes todynamically control the vehicle. By using brakes in addition to steeringcontrol some control benefits may be achieved. For example, yaw controland rollover control may be simultaneously accomplished.

Speed sensor 30 may be one of a variety of speed sensors known to thoseskilled in the art. For example, a suitable speed sensor may include asensor at every wheel that is averaged by controller 26. As will bedescribed below, the controller 26 translates the wheel speeds into thespeed of the vehicle.

Referring now to FIG. 4, a method of operating a safety system using acorrected vehicle velocity is determined. In step 60 the wheel speedsensors are read. In one embodiment each wheel has a separate speedsensor.

The wheel speed sensor outputs usually are calibrated for providing thelinear directional velocities V_(lf), V_(rf), V_(lr) and V_(rr) bymultiplying the wheel rotational angular speeds with a nominal rollingradius of the wheels. The variables ω_(lf-sensor), ω_(rf-sensor),ω_(lr-sensor) and ω_(rr-sensor) are the wheel angular velocity at theleft-front corner, right-front corner, left-rear corner and rear-rightcorner respectively. The nominal rolling radius (typically used in ABS)for calculating wheel speeds from the wheel rotational rates is r₀.Thus, the linear directional velocities may be represented by:v_(lf)=ω_(lf-sensor)r₀v_(rf)=ω_(rf-sensor)r₀v_(lr)=ω_(lr-sensor)r₀v_(rr)=ω_(rr-sensor)r₀   (3)

Notice that the wheels have different rolling radii than r₀. Hence, inorder to accurately calculate the actual linear velocities at the fourcorners, correction factors need to be added. The individual correctionfactors are denoted as K_(lf), K_(rf), K_(lr) and K_(rr) for theleft-front, right-front, left-rear and rear-right corners, respectively.Thus, the linear directional velocities may then be represented by:v_(lf)=K_(lf)ω_(lf-sensor)r₀v_(rf)=K_(rf)ω_(rf-sensor)r₀v_(lr)=K_(lr)ω_(lr-sensor)r₀v_(rr)=K_(rr)ω_(rr-sensor)r₀   (4)

Notice also that the wheels experience not only the rotational motionbut also the linear sliding motion, or longitudinal slip. The slip iscaused by the relative motion between the wheel and the road at thecontact patch (CP). The longitudinal velocities of the relative motionsat the contact patches are denoted as v_(cp-lf), v_(cp-rf, v) _(cp-lr)and v_(cp-rr), then the vehicle corner velocities can be expressed asthe sums of two speeds as in the followingV_(lf)=v_(cp-lf)+v_(lf)V_(rf)=v_(cp-rf)+v_(rf)V_(lr)=v_(cp-lr)+v_(lr)V_(rr)=v_(cp-rr)+v_(rr)   (5)

The longitudinal and lateral velocities of the vehicle may be determinedin step 62 from the sensors, or they may be calculated as in Forddisclosure 201-1057 filed simultaneously herewith, or even a roughestimation by averaging certain variables calculated from wheel speeds.This may be a rough estimate or average but, as mentioned above, doesnot take into consideration the rolling radius or other factors.ConsiderV_(y)=V_(x) tan (β)   (6)where β is the vehicle side slip angle V_(y) is the lateral velocity ofthe vehicle and V_(x) is the longitudinal velocity of the vehicle. Instep 64, the front steering angle 8 is determined. Then, the individualcorrection factors K_(lf), K_(rf), K_(lr) and K_(rr) for each wheel canbe calculated in step 66 as $\begin{matrix}{{\kappa_{lf} = {\frac{{V_{x}\lbrack {{\cos(\delta)} + {{\tan(\beta)}{\sin(\delta)}}} \rbrack} + {\omega_{z}\lbrack {{l_{f}{\sin(\delta)}} - {t_{f}{\cos(\delta)}}} \rbrack}}{\omega_{{lf} - {sensor}}r_{0}} - \frac{v_{{cp} - {lf}}}{\omega_{{lf} - {sensor}}r_{0}}}}{\kappa_{rf} = {\frac{{V_{x}\lbrack {{\cos(\delta)} + {{\tan(\beta)}{\sin(\delta)}}} \rbrack} + {\omega_{z}\lbrack {{l_{f}{\sin(\delta)}} + {t_{f}{\cos(\delta)}}} \rbrack}}{\omega_{{rf} - {sensor}}r_{0}} - \frac{v_{{cp} - {rf}}}{\omega_{{rf} - {sensor}}r_{0}}}}{\kappa_{lr} = {\frac{V_{x} - {\omega_{z}t_{r}}}{\omega_{{lr} - {sensor}}r_{0}} - \frac{v_{{cp} - {lr}}}{\omega_{{lr} - {sensor}}r_{0}}}}{\kappa_{rr} = {\frac{V_{x} + {\omega_{z}t_{r}}}{\omega_{{rr} - {sensor}}r_{0}} - \frac{v_{{cp} - {rr}}}{\omega_{{rr} - {sensor}}r_{0}}}}} & (7)\end{matrix}$

The product term tan (β) sin (δ) is negligible in comparison to cos (δ),hence equation (7) may be further simplified to the following, which isindependent of the vehicle side slip angle β $\begin{matrix}{{\kappa_{lf} \approx {\frac{{V_{x}{\cos(\delta)}} + {\omega_{z}\lbrack {{l_{f}{\sin(\delta)}} - {t_{f}{\cos(\delta)}}} \rbrack}}{\omega_{{lf} - {sensor}}r_{0}} - \frac{v_{{cp} - {lf}}}{\omega_{{lf} - {sensor}}r_{0}}}}{\kappa_{rf} \approx {\frac{{V_{x}{\cos(\delta)}} + {\omega_{z}\lbrack {{l_{f}{\sin(\delta)}} + {t_{f}{\cos(\delta)}}} \rbrack}}{\omega_{{rf} - {sensor}}r_{0}} - \frac{v_{{cp} - {rf}}}{\omega_{{rf} - {sensor}}r_{0}}}}{\kappa_{lr} = {\frac{V_{x} - {\omega_{z}t_{r}}}{\omega_{{lr} - {sensor}}r_{0}} - \frac{v_{{cp} - {lr}}}{\omega_{{lr} - {sensor}}r_{0}}}}{\kappa_{rr} = {\frac{V_{x} + {\omega_{z}t_{r}}}{\omega_{{rr} - {sensor}}r_{0}} - \frac{v_{{cp} - {rr}}}{\omega_{{rr} - {sensor}}r_{0}}}}} & (8)\end{matrix}$

In the case of small wheel longitudinal slip ratios, the longitudinalvelocities v_(cp-lf), v_(cp-rf), v_(cp-lr) and v_(cp-rr) of the relativemotions at the contact patches are close to zero, and equation (8) canbe further simplified as the following $\begin{matrix}{{\kappa_{lf} \approx \frac{{V_{x}{\cos(\delta)}} + {\omega_{z}\lbrack {{l_{f}{\sin(\delta)}} - {t_{f}{\cos(\delta)}}} \rbrack}}{\omega_{{lf} - {sensor}}r_{0}}}{\kappa_{rf} \approx \frac{{V_{x}{\cos(\delta)}} + {\omega_{z}\lbrack {{l_{f}{\sin(\delta)}} + {t_{f}{\cos(\delta)}}} \rbrack}}{\omega_{{rf} - {sensor}}r_{0}}}{\kappa_{lr} = \frac{V_{x} - {\omega_{z}t_{r}}}{\omega_{{lr} - {sensor}}r_{0}}}{\kappa_{rr} = \frac{V_{x} + {\omega_{z}t_{r}}}{\omega_{{rr} - {sensor}}r_{0}}}} & (8)\end{matrix}$

The digital value of the above wheel speed individual correction factorsK_(lf), K_(rf), K_(lr) and K_(rr) at the time instant t=kΔT areK_(lf) _(k) , K_(rf) _(k) , K_(lr) _(k) and K_(rr) _(k)then learning algorithms can be used to calculate the average correctionfactors. The correction factors are determined using an iterativeprocess that is updated every N calculation samples in the followinglearning example. Notice that this is a conditional computation which isconducted only if the wheel's longitudinal slip ratios are small.$\begin{matrix}{{START}\quad\text{}{{{{if}\quad k} < {N\quad{\overset{\_}{\kappa}}_{{lf}_{k + 1}}}} = {{{\overset{\_}{\kappa}}_{{lf}_{k}} + {\frac{\kappa_{{lf}_{k + 1}}}{N}\quad{\overset{\_}{\kappa}}_{{rf}_{k + 1}}}} = {{{\overset{\_}{\kappa}}_{{rf}_{k}} + {\frac{\kappa_{{rf}_{k + 1}}}{N}\quad{\overset{\_}{\kappa}}_{{lr}_{k + 1}}}} = {{{\overset{\_}{\kappa}}_{{lr}_{k}} + {\frac{\kappa_{{lr}_{k + 1}}}{N}\quad{\overset{\_}{\kappa}}_{{rr}_{k + 1}}}} = {{{\overset{\_}{\kappa}}_{{rr}_{k}} + {\frac{\kappa_{{rr}_{k + 1}}}{N}\quad k}} = {{k + {1{{elseif}\quad k}}} = {{N\quad k} = {{0\quad{\overset{\_}{\kappa}}_{lf}} = {{{\overset{\_}{\kappa}}_{{lf}_{N + 1}}\quad{\overset{\_}{\kappa}}_{rf}} = {{{\overset{\_}{\kappa}}_{{rf}_{N + 1}}\quad{\overset{\_}{\kappa}}_{lr}} = {{{\overset{\_}{\kappa}}_{{lr}_{N + 1}}\quad{\overset{\_}{\kappa}}_{rr}} = {{\overset{\_}{\kappa}}_{{rr}_{N + 1}}\quad{go}\quad{to}\quad{START}}}}}}}}}}}}}} & (10)\end{matrix}$

Using the above learning algorithm, corrected wheel speeds at each wheelcan be determined in step 66 based upon the learned correction factor.{circumflex over (v)}_(lf) _(k) = K _(lf)r₀ω_(lf-sensor) _(k){circumflex over (v)}_(rf) _(k) = K _(rf)r₀ω_(rf-sensor) _(k){circumflex over (v)}_(lr) _(k) = K _(lr)r₀ω_(lr-sensor) _(k){circumflex over (v)}_(rr) _(k) = K _(rr)r₀ω_(rr-sensor) _(k)   (11)

Notice that the above learning algorithm only corrects the individualwheel speeds. There are cases when the average rolling radii of the fourwheels are reduced together due to vehicle loading change. Feeding backthe above corrected wheel speeds to the algorithms used in vehicledynamics control will provide a vehicle reference velocity{circumflex over (V)}_(ref)in step 70 which needs to be further calibrated against the availablevehicle longitudinal acceleration sensor signal.

Consider that the actual vehicle reference velocity isV_(ref)=K{circumflex over (V)}_(ref)   (12)where K is the global correction factor due to the total vehicleloading. K is usually a slow time varying parametersK{circumflex over (V)}_(ref)=a_(x)−gθ_(y)   (13)where θ_(y) is the vehicle pitch angle generated from a pitch anglesensor or calculated from the pitch rate sensor signal.

In step 72, the longitudinal acceleration a_(x) is determined. Then, thefollowing variables are defined $\begin{matrix}{{\overset{\Cap}{V} = \begin{bmatrix}{\overset{\Cap}{v}}_{{ref}_{1}} \\{\overset{\Cap}{v}}_{{ref}_{2}} \\\vdots \\{\overset{\Cap}{v}}_{{ref}_{N}}\end{bmatrix}},{A_{x} = \begin{bmatrix}a_{x_{1}} \\a_{x_{2}} \\\vdots \\a_{x_{N}}\end{bmatrix}},{\Theta_{y} = \begin{bmatrix}\theta_{y_{1}} \\\theta_{y_{2}} \\\vdots \\\theta_{y_{N}}\end{bmatrix}},} & (14)\end{matrix}$

Then a least square computation of the correction factor due to loadingcan be determined in step 74 as the following:{circumflex over (K)}=inv({circumflex over (V)}^(T){circumflex over(V)}){circumflex over (V)}^(T)[A_(x)−gΘ_(y)]  (15)or in the following form $\begin{matrix}{\hat{K} = \frac{\sum\limits_{k = {M + 1}}^{M + N}\quad{{\overset{\Cap}{v}}_{{ref}_{k}}( {a_{x_{k}} - {g\quad\theta_{y_{k}}}} )}}{\sum\limits_{k = {M + 1}}^{M + N}\quad{\overset{\Cap}{v}}_{{ref}_{k}}^{2}}} & (16)\end{matrix}$

Notice that the global correction factor{circumflex over (K)}

is updated every N computational samples when the wheels have smalllongitudinal slip ratios. The digital implementation of equation (16)can be obtained as in the following where V_(k+1) is the updatedreference velocity determined in step 76. START   if  k < N$\quad{A_{k + 1} = {A_{k} + {{\overset{\Cap}{v}}_{{ref}_{k + 1}}( {a_{x_{k + 1}} - {g\quad\theta_{y_{k + 1}}}} )}}}$$\quad{V_{k + 1} = {V_{k} + {{\overset{\Cap}{v}}_{{ref}_{k + 1}}{\overset{\Cap}{v}}_{{ref}_{k + 1}}}}}$  k = k + 1elseif  k = N$\quad{\hat{\kappa} = \frac{A_{N + 1}}{V_{N + 1}}}$   k = 0  go  to  START

The final corrected wheel speed sensor signals may be corrected by theaforementioned factors can also be obtained as the following:{circumflex over (v)}_(lf) _(k) ={circumflex over (K)} K_(lf)r₀ω_(lf-sensor) _(k){circumflex over (v)}_(rf) _(k) ={circumflex over (K)} K_(rf)r₀ω_(rf-sensor) _(k){circumflex over (v)}_(lr) _(k) ={circumflex over (K)} K_(lr)r₀ω_(lr-sensor) _(k){circumflex over (v)}_(rr) _(k) ={circumflex over (K)} K_(rr)r₀ω_(rr-sensor) _(k)   (17)

Once the corrected final vehicle reference velocity is determined, thesafety system 40 may be controlled using the compensated velocityvalues.

While particular embodiments of the invention have been shown anddescribed, numerous variations and alternate embodiments will occur tothose skilled in the art. Accordingly, it is intended that the inventionbe limited only in terms of the appended claims.

1. A control system for controlling a safety system of an automotivevehicle comprising: a plurality of wheel speed sensors generating aplurality of wheel velocity signals; a steering angle sensor generatinga steering actuator angle signal; a yaw rate sensor generating a yawrate signal; a lateral longitudinal acceleration sensor generating alateral longitudinal acceleration signal; and a controller coupled tothe plurality of wheel speed sensors, the steering actuator anglesensor, the yaw rate sensor, the lateral longitudinal accelerationsensor, said controller generating a final reference vehicle velocity inresponse to the plurality of wheel velocity signals, the steering anglesignal, the yaw rate signal and the lateral longitudinal accelerationsignal, said controller controlling the safety system in response to thefinal reference vehicle velocity.
 2. A control system as recited inclaim 1 wherein the safety system comprises a rollover control system.3. A control system as recited in claim 1 wherein the safety systemcomprises a yaw control system.
 4. A control system as recited in claim1 wherein the safety system comprises an antilock brake system.
 5. Acontrol system as recited in claim 1 wherein the final reference vehiclevelocity is determined in response to a learning function.
 6. A controlsystem for an automotive vehicle comprising: a plurality of wheel speedsensors generating a plurality of wheel velocity signals; a laterallongitudinal acceleration sensor generating a lateral longitudinalacceleration signal; a safety system; and a controller coupled to theplurality of wheel speed sensors, the lateral longitudinal accelerationsensor and the safety system, said controller determining a preliminarylongitudinal velocity of the vehicle from the plurality of wheelvelocity signals, determining a plurality of correction factors for theplurality of wheel velocity signals, determining a vehicle referencevelocity in response to the plurality of correction factors, theplurality of wheel velocities and the preliminary longitudinal velocity,determining a vehicle reference velocity correction factor in responseto the lateral longitudinal acceleration, determining a final referencevelocity in response to the velocity correction factor and the vehiclereference velocity, said controller controlling the safety system inresponse to the final reference vehicle velocity.
 7. A control system asrecited in claim 1 wherein the safety system comprises a rollovercontrol system.
 8. A control system as recited in claim 1 wherein thesafety system comprises a yaw control system.
 9. A control system asrecited in claim 1 wherein the safety system comprises an antilock brakesystem.
 10. A control system as recited in claim 1 wherein determining aplurality of correction factors is performed using a learning function.11. A control system as recited in claim 1 10 wherein the learningfunction averages N correction factors, where N is an integer.
 12. Acontrol system as recited in claim 1 further comprising said controllerdetermining a nominal rolling radius, wherein the wheel velocity is afunction of vehicle speed.
 13. A method of controlling a safety systemfor an automotive vehicle having a plurality of wheels comprising:determining a plurality of wheel velocities for the plurality of wheels;determining a preliminary longitudinal velocity of the vehicle from theplurality of wheel velocities; determining a plurality of correctionfactors for the plurality of wheel velocities for the plurality ofwheels; determining a vehicle reference velocity in response to theplurality of correction factors, the plurality of wheel velocities andthe preliminary longitudinal velocity; determining a laterallongitudinal acceleration; determining a vehicle reference velocitycorrection factor in response to the lateral longitudinal acceleration;determining a final reference velocity in response to the vehiclereference velocity correction factor and the vehicle reference velocity;and controlling the safety system in response to the final referencevelocity.
 14. A method as recited in claim 13 further comprisingdetermining a yaw rate determining a plurality of preliminary laterallongitudinal velocity of the vehicle from the plurality of wheel speedsand the yaw rate.
 15. A method as recited in claim 13 further comprisingdetermining a front steering angle, wherein determining a plurality ofcorrection factors are determined in response to the front steeringangle.
 16. A method as recited in claim 13 wherein said safety systemcomprises at least one selected from a rollover stability controlsystem, a yaw control system, a traction control system or an antilockbrake control system.
 17. A method as recited in claim 13 furthercomprising using a learning function in the step of determining aplurality of correction factors.
 18. A method of controlling a safetysystem for an automotive vehicle having a plurality of wheelscomprising: determining a plurality of wheel velocities for theplurality of wheels; determining a yaw rate; determining a preliminarylongitudinal velocity of the vehicle from the plurality of wheelvelocities and the yaw rate; determining a front steering angle;determining a plurality of correction factors for the plurality ofpreliminary wheel speeds in response to the front steering angle;determining a vehicle reference velocity in response to the plurality ofcorrection factors and the plurality of correction factors and thepreliminary longitudinal velocity.
 19. A method as recited in claim 18further comprising determining a lateral longitudinal acceleration;determining a velocity correction factor in response to the laterallongitudinal acceleration; and determining a final reference velocity inresponse to the velocity correction factor and the vehicle referencevelocity.
 20. A method as recited in claim 18 further comprising using alearning function in the step of determining a plurality of correctionfactors.
 21. A method as recited in claim 18 wherein said safety systemcomprises at least one selected from a rollover stability controlsystem, a yaw control system, a traction control system or an antilockbrake control system.